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On fuzzy linear projection equation and applications

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Abstract

This paper introduces the concept of fuzzy projection of a fuzzy number on a set of fuzzy numbers based on r-cut approach. It is proved that the projection of a fuzzy number on the set of all fuzzy numbers is itself and under a special metric, the proposed fuzzy projection is a non-expansive mapping. By using this definition, the concept of fuzzy linear projection equation is defined and to solve it, a numerical method is applied. Based on the proposed algorithm and as an important application, two different types of system of fuzzy linear equations with fuzzy variables are solved. Numerical results illustrate the applicabilities of proposed approach.

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Acknowledgments

The authors are thankful to the unknown referees for their valuable and informative comments that have significantly improved the quality of the paper. They also appreciate the Editors and Editor in Chief for their valuable suggestions.

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Correspondence to Sohrab Effati.

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This study was not funded by any grant.

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The authors declare that they have no conflict of interest.

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Pakdaman, M., Effati, S. On fuzzy linear projection equation and applications. Fuzzy Optim Decis Making 15, 219–236 (2016). https://doi.org/10.1007/s10700-015-9222-8

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